position-in-spiral.py

gistfile1.txt

# got a huge ammount of help from https://stackoverflow.com/questions/11550153/determine-position-of-number-in-a-grid-of-numbers-centered-around-0-and-increasi

def sequence(i):
  n = 2 * i - 1
  return n * n

def layer(i):
  return math.floor((math.sqrt(i) + 1) / 2)

def length(i):
  return 8 * i

def sector(i):
  return math.floor(4 * (i - sequence(layer(i))) / length(layer(i)))

def position(i):
  l = layer(i)
  s = sector(i)
  offset = i - sequence(l) - s * length(l) // 4
  if s == 0.0:
    return -l, -l + offset + 1
  if s == 1.0:
    return -l + offset - 1, l
  if s == 2.0:
    return l, l - offset - 1
  return l - offset - 1, -l
  
pos = position(265148) # everything is minus 1 so 265149 -> 265148
steps = abs(pos[0]) + abs(pos[1])